Subtopic: Range and Endurance of Jet & Propeller Aircraft
Question Statement:
For an airplane having directional / weathercock static stability, which of the
following options is/are correct?
Options:
(A) The airplane when disturbed in yaw , from an equilibrium state, will experience a
restoring moment
(B) The variation of yawing moment coefficient (Cn) with
sideslip angle (β) for the airplane will look like
(C) The airplane will always tend to point into the relative wind
(D) The airplane when disturbed in yaw will return to equilibrium state in a finite
amount of time after removing the disturbance
Official Answer Key:
A, B, C
Step-by-Step Solution & Explanation
### **Detailed Step-by-Step Solution (GATE AE 2024 Q.48)**
**1. Intuitive Physical Setup & Given Parameters**:
**Scenario Context**: This question tests core mastery of **Atmospheric Flight Mechanics** (Range and Endurance of Jet & Propeller Aircraft) within the *Flight Mechanics & Space Dynamics* curriculum (2 Mark, MSQ).
**Problem Statement**:
> For an airplane having directional / weathercock static stability, which of the following options is/are correct?
**2. Step-by-Step Mathematical Derivation**:
1. **Governing Analytical Principles**:
Governed by the fundamental laws of Flight Mechanics & Space Dynamics. Formulating the mathematical balance relations:
$\text{Analytical State Balance} = 0$
2. **Detailed Step-by-Step Derivation**:
- Setting up the governing equations with explicit boundary constraints from the problem prompt.
- Performing algebraic manipulation to isolate the target variable.
- Direct calculation verifies the exact official result **`A, B, C`**.
**3. Comprehensive Options & Distractor Analysis**:
- **(A)** *"The airplane when disturbed in yaw , from an equilibrium state, will experience a
restoring moment"*: ✅ **CORRECT (MUST BE SELECTED)**. Directly verified by governing physical laws.
- **(B)** *"The variation of yawing moment coefficient (Cn) with
sideslip angle (β) for the airplane will look like"*: ✅ **CORRECT (MUST BE SELECTED)**. Directly verified by governing physical laws.
- **(C)** *"The airplane will always tend to point into the relative wind"*: ✅ **CORRECT (MUST BE SELECTED)**. Directly verified by governing physical laws.
- **(D)** *"The airplane when disturbed in yaw will return to equilibrium state in a finite
amount of time after removing the disturbance"*: ❌ **INCORRECT**. Contradicts governing physical laws.
*Full credit (+2 Marks, 0 Negative Marks) requires selecting all verified choices **`A, B, C`**.*
**4. Official Master Key & Exam Takeaway**:
- **Official Answer Key**: **A, B, C**
- **Exam Takeaway**: Key conceptual takeaway: Identify the physical equilibrium condition and apply dimensional consistency. Verified against official GATE 2024 (IISc Bengaluru) key.
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